Gibbs free energy

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1800s, Josiah Willard Gibbs, (1839-1903) submitted scientific papers which mathematically combined both enthalpy and entropy (the measure of energy release and disorder in a system respectively) that also incorporates the second law of thermodynamics:

Entropy can never decrease, only increase for a reaction to take place.

in order to measure the amount of free energy present within any given system.[1]

According to the second law of thermodynamics, a chemical reaction can only proceed spontaneously if there is a net increase in disorder I the universe. An increase in disorder of the universe can be expressed most conveniently in terms of a quantity called the free energy, G of a system. The value of G is of interest only when a system undergoes a change, such as a reaction, in such a case the value of delta G is critical. Energetically favourable reactions are those that decrease free energy and have a negative delta G, these reactions  add more to disorder to the universe.[2]

Contents

Why doesn't free energy = enthalpy - entropy?

Reasoning behind Gibbs equation

The signs for enthalpy and entropy must be opposites to each other, "because one function tends to a maximum and the other tends to a minimum." [3]As a consequence the one equation proposed for this "unknown energy function"[4] could be: ====

X= U - S
(where X = Function, U = Enthalpy, S = Entropy) [5]

Although this must be carried out under standard conditions, so U must be substituted for an H to demonstrate a constant pressure. (of 1atm) In addition to this, the units are wrong in our current equation; as we know, enthalpy is measure in joules (J) of energy, entropy on the other hand is measured in joules per kelvin. (J K-1) Thus, we must also multiply entropy (S) by temperature in Kelvin. (T) Giving us the following equation when delta symbols are incorporate to represent that this function is for free energy changes:

dG = dH - dTS
(where G = Free energy, H = Enthalpy, S = Entropy, T = Temperature, d = Change in associated function) [6]

Application

We can now determine each individual component of this equation, enthalpy change being determined via "calorimetric measurment" [7] to give us our value for dH; entropy can then be found if dG and temperature are known, the opposite can be said for determining dG itself with dS being our known value instead. For a reaction to be possible, it has been stated that the entropy of the universe is always increased. Consequently for a reaction to take place, dG must always be negative, with dS in the the equation for free energy exceeding that of the enthalpy change dH.

References

  1. Sadi, Carnot. (2013). Willard Gibbs. Available: http://www.eoht.info/page/Willard+Gibbs. Last accessed 28th Nov 2013.
  2. Alberts et al.Molecular Biology of the Cell,(2008) 5th Ed. Page 75
  3. Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley and Sons, Inc.. p84-90.
  4. Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley and Sons, Inc.. p84-90.
  5. Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley and Sons, Inc.. p84-90.
  6. Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley and Sons, Inc.. p84-90.
  7. Donald W. Rogers (2010). Concise Physical Chemistry. Hoboken: John Wiley and Sons, Inc.. p84-90.
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